Block #260,557

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/14/2013, 10:31:21 AM · Difficulty 9.9772 · 6,549,902 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

98dba4bbb783ef467b5cea416d071c14ec95c767ed707631788f45005d941ef1

View on Chainz ↗

Height

#260,557

Difficulty

9.977157

Transactions

Size

904 B

Version

Bits

09fa26f0

Nonce

3,039

Timestamp

11/14/2013, 10:31:21 AM

Confirmations

6,549,902

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

e720e249f8ab6f3e2f2f851d9bcf2f1abb9be3582d7bc347f00af75ace8bba9f

Transactions (2)

Coinbasecbf71e37d0827a…3f8375332a02bd

1 in → 2 out10.0500 XPM142 B

AdGRRh1e…QmctLb24 AU6kq4CL…dQBLvxLp

a0e5ee541b7dfa…1930cd7223efa2

4 in → 2 out331.2920 XPM671 B

AX9wKBzk…d5CdhuBL AbHZM4d2…8YBLXYao

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.

2.679 × 10⁹⁶(97-digit number)

26794197508206735462…47668936243039727359

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

2.679 × 10⁹⁶(97-digit number)

26794197508206735462…47668936243039727359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.679 × 10⁹⁶(97-digit number)

26794197508206735462…47668936243039727361

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

5.358 × 10⁹⁶(97-digit number)

53588395016413470924…95337872486079454719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.358 × 10⁹⁶(97-digit number)

53588395016413470924…95337872486079454721

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

1.071 × 10⁹⁷(98-digit number)

10717679003282694184…90675744972158909439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.071 × 10⁹⁷(98-digit number)

10717679003282694184…90675744972158909441

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

2.143 × 10⁹⁷(98-digit number)

21435358006565388369…81351489944317818879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.143 × 10⁹⁷(98-digit number)

21435358006565388369…81351489944317818881

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

4.287 × 10⁹⁷(98-digit number)

42870716013130776739…62702979888635637759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.287 × 10⁹⁷(98-digit number)

42870716013130776739…62702979888635637761

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #260,557

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