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Block #593,881

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/19/2014, 2:00:57 AM Β· Difficulty 10.9395 Β· 6,214,264 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
4978a73cc84f27bea6c0c2b10663655415aef90d926d5f8398518c24bea4daff
View on Chainz β†—

Height

#593,881

Difficulty

10.939501

Transactions

3

Size

807 B

Version

2

Bits

0af08323

Nonce

17,755,017

Timestamp

6/19/2014, 2:00:57 AM

Confirmations

6,214,264

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

957f765a471c5ff0ac3e1555987fc6f51c2553e1e715650181d98645e34c923e
Transactions (3)
Coinbase64ab6d4dc6e5e1…03644f826a4aa7
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
c1835648a6f6d6…58deba795dfe06
2 in β†’ 2 out10.9575 XPM374 B
AaU9J1Lk…4e47uLfqAHNx5S5s…F9PkHfVq
af7226f7a24498…78c67db635e45f
1 in β†’ 2 out6.7317 XPM226 B
AYU1Ynxb…6LNs2ZYMAVkWqhMg…N2DcEs7M
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.262 Γ— 10⁹⁷(98-digit number)
22622914111596097632…14871170362830095759
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.262 Γ— 10⁹⁷(98-digit number)
22622914111596097632…14871170362830095759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.262 Γ— 10⁹⁷(98-digit number)
22622914111596097632…14871170362830095761
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.524 Γ— 10⁹⁷(98-digit number)
45245828223192195265…29742340725660191519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.524 Γ— 10⁹⁷(98-digit number)
45245828223192195265…29742340725660191521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
9.049 Γ— 10⁹⁷(98-digit number)
90491656446384390530…59484681451320383039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.049 Γ— 10⁹⁷(98-digit number)
90491656446384390530…59484681451320383041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.809 Γ— 10⁹⁸(99-digit number)
18098331289276878106…18969362902640766079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.809 Γ— 10⁹⁸(99-digit number)
18098331289276878106…18969362902640766081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.619 Γ— 10⁹⁸(99-digit number)
36196662578553756212…37938725805281532159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.619 Γ— 10⁹⁸(99-digit number)
36196662578553756212…37938725805281532161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
7.239 Γ— 10⁹⁸(99-digit number)
72393325157107512424…75877451610563064319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,709,203 XPMΒ·at block #6,808,144 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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