Block #260,577

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/14/2013, 11:17:50 AM · Difficulty 9.9771 · 6,548,848 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7d7a1f24d1c63607b9695575d488c37db3987036a9172ba6ccb093a37ff9496b

View on Chainz ↗

Height

#260,577

Difficulty

9.977056

Transactions

Size

1.00 KB

Version

Bits

09fa2055

Nonce

13,077

Timestamp

11/14/2013, 11:17:50 AM

Confirmations

6,548,848

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

903725e59491b5a364bb2e555576c4583ed0f6023ada01c21c60c17ba3159c0d

Transactions (4)

Coinbasec61efd584512da…d357fb5c85613f

1 in → 2 out10.0600 XPM142 B

AdGRRh1e…QmctLb24 AU6kq4CL…dQBLvxLp

fb99d4a84b9111…cf5f814750460b

1 in → 1 out10.0600 XPM157 B

ATV4M1CV…dd9zw8nH

e1fbbecf470549…0713ae984cc6eb

1 in → 4 out10.0400 XPM260 B

Ae4ssmDA…vZSZMfbk AVKfZvtY…sCa4NTcM AeKNrjNj…1NEq95Ta AMuPGPXT…eMMNvd8v

df62c1ad1df898…a8f328c507c88a

2 in → 2 out2.0108 XPM373 B

ANPEvQmE…zboVZPkB ANcPENP1…UGn51ywY

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.

2.106 × 10⁹⁸(99-digit number)

21069578756770417107…22711547580793804799

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

2.106 × 10⁹⁸(99-digit number)

21069578756770417107…22711547580793804799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.106 × 10⁹⁸(99-digit number)

21069578756770417107…22711547580793804801

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

4.213 × 10⁹⁸(99-digit number)

42139157513540834214…45423095161587609599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.213 × 10⁹⁸(99-digit number)

42139157513540834214…45423095161587609601

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

8.427 × 10⁹⁸(99-digit number)

84278315027081668428…90846190323175219199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.427 × 10⁹⁸(99-digit number)

84278315027081668428…90846190323175219201

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

1.685 × 10⁹⁹(100-digit number)

16855663005416333685…81692380646350438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.685 × 10⁹⁹(100-digit number)

16855663005416333685…81692380646350438401

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

3.371 × 10⁹⁹(100-digit number)

33711326010832667371…63384761292700876799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #260,577

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