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Block #2,451,899

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/1/2018, 2:37:13 AM Β· Difficulty 10.9498 Β· 4,391,025 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
99a3665b2a18aa9b50b0ee23dfd1b270b3902ba8c877f73a019a32f1ef718ac3
View on Chainz β†—

Height

#2,451,899

Difficulty

10.949750

Transactions

1

Size

199 B

Version

2

Bits

0af322d3

Nonce

60,330,134

Timestamp

1/1/2018, 2:37:13 AM

Confirmations

4,391,025

Mined by

⛏️ P2SHAYtZ2oEzXkHoehfWLGhSQB7ki8MLBgJ6KJ

Merkle Root

5591fbc34f81aa813c312f3fabe5cb5790256727ac6677fd691c1af4e594efc2
Transactions (1)
Coinbase5591fbc34f81aa…1c1af4e594efc2
1 in β†’ 1 out8.3300 XPM110 B
AYtZ2oEz…MLBgJ6KJ
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.

1.938 Γ— 10⁹³(94-digit number)
19386334413033401216…77445289221529221119
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
1.938 Γ— 10⁹³(94-digit number)
19386334413033401216…77445289221529221119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.938 Γ— 10⁹³(94-digit number)
19386334413033401216…77445289221529221121
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
3.877 Γ— 10⁹³(94-digit number)
38772668826066802433…54890578443058442239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.877 Γ— 10⁹³(94-digit number)
38772668826066802433…54890578443058442241
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
7.754 Γ— 10⁹³(94-digit number)
77545337652133604866…09781156886116884479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.754 Γ— 10⁹³(94-digit number)
77545337652133604866…09781156886116884481
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
1.550 Γ— 10⁹⁴(95-digit number)
15509067530426720973…19562313772233768959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.550 Γ— 10⁹⁴(95-digit number)
15509067530426720973…19562313772233768961
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
3.101 Γ— 10⁹⁴(95-digit number)
31018135060853441946…39124627544467537919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.101 Γ— 10⁹⁴(95-digit number)
31018135060853441946…39124627544467537921
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
6.203 Γ— 10⁹⁴(95-digit number)
62036270121706883893…78249255088935075839
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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