Block #2,646,156

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 5:43:05 AM · Difficulty 11.7455 · 4,184,568 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

57da3827b674889681d2fed215cb1edc3245b4359320b772e8475b0bdb25b2f5

View on Chainz ↗

Height

#2,646,156

Difficulty

11.745463

Transactions

Size

904 B

Version

Bits

0bbed6a9

Nonce

1,260,525,803

Timestamp

5/3/2018, 5:43:05 AM

Confirmations

4,184,568

Mined by

⛏️ P2SHAczck1wXJFLfBSgYnR3JQBccaGDGjyqTxJ

Merkle Root

bcd94a4e6aeceb70e1e084555acf6ac3311b9f5be8d25f61e6f7563f11052d05

Transactions (2)

Coinbase9ec622c93a4708…3ae910b983f765

1 in → 1 out7.2500 XPM110 B

Aczck1wX…DGjyqTxJ

1bbc5949132dfa…d27320c3f382b9

4 in → 3 out14.1352 XPM704 B

ASk9H3sY…qUG8r1d4 APi8C85f…Lg5MDiei ANF5hJrW…cuF7SAG4

Prime Chain Origin

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

3.735 × 10⁹⁵(96-digit number)

37359335029945748996…86203646285594763999

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

3.735 × 10⁹⁵(96-digit number)

37359335029945748996…86203646285594763999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.735 × 10⁹⁵(96-digit number)

37359335029945748996…86203646285594764001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.471 × 10⁹⁵(96-digit number)

74718670059891497992…72407292571189527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.471 × 10⁹⁵(96-digit number)

74718670059891497992…72407292571189528001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.494 × 10⁹⁶(97-digit number)

14943734011978299598…44814585142379055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.494 × 10⁹⁶(97-digit number)

14943734011978299598…44814585142379056001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.988 × 10⁹⁶(97-digit number)

29887468023956599197…89629170284758111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.988 × 10⁹⁶(97-digit number)

29887468023956599197…89629170284758112001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

5.977 × 10⁹⁶(97-digit number)

59774936047913198394…79258340569516223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.977 × 10⁹⁶(97-digit number)

59774936047913198394…79258340569516224001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.195 × 10⁹⁷(98-digit number)

11954987209582639678…58516681139032447999

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,646,156

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