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Block #2,944,833

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/29/2018, 7:02:45 PM Β· Difficulty 11.3941 Β· 3,898,502 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c8309fc7a13550310566459ce9253d54c9716c8afccf71eadf73ab4522c1a526
View on Chainz β†—

Height

#2,944,833

Difficulty

11.394113

Transactions

1

Size

201 B

Version

2

Bits

0b64e496

Nonce

1,620,168,037

Timestamp

11/29/2018, 7:02:45 PM

Confirmations

3,898,502

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

c6c3abf2e5a6a1bcec9488489e0b94b434c4b8e5b3b34a1ae81cf014abd4557a
Transactions (1)
Coinbasec6c3abf2e5a6a1…1cf014abd4557a
1 in β†’ 1 out7.6900 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.560 Γ— 10⁹⁸(99-digit number)
15608507634119668266…48307350830517452799
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
1.560 Γ— 10⁹⁸(99-digit number)
15608507634119668266…48307350830517452799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.560 Γ— 10⁹⁸(99-digit number)
15608507634119668266…48307350830517452801
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
3.121 Γ— 10⁹⁸(99-digit number)
31217015268239336532…96614701661034905599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.121 Γ— 10⁹⁸(99-digit number)
31217015268239336532…96614701661034905601
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
6.243 Γ— 10⁹⁸(99-digit number)
62434030536478673065…93229403322069811199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.243 Γ— 10⁹⁸(99-digit number)
62434030536478673065…93229403322069811201
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
1.248 Γ— 10⁹⁹(100-digit number)
12486806107295734613…86458806644139622399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.248 Γ— 10⁹⁹(100-digit number)
12486806107295734613…86458806644139622401
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
2.497 Γ— 10⁹⁹(100-digit number)
24973612214591469226…72917613288279244799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.497 Γ— 10⁹⁹(100-digit number)
24973612214591469226…72917613288279244801
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
4.994 Γ— 10⁹⁹(100-digit number)
49947224429182938452…45835226576558489599
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:57,991,042 XPMΒ·at block #6,843,334 Β· updates every 60s
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