Block #726,335

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/17/2014, 8:41:32 PM · Difficulty 10.9610 · 6,068,248 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b99a05aad6f869594406397e58ac86c199eba31e358cd92262c76e23c6e8f2c3

View on Chainz ↗

Height

#726,335

Difficulty

10.960955

Transactions

Size

2.21 KB

Version

Bits

0af6011f

Nonce

656,573,055

Timestamp

9/17/2014, 8:41:32 PM

Confirmations

6,068,248

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6429e70a0ad7d8d8e36ddd95dce634a01df5b1dcbd063b092eb3d990fa295b6f

Transactions (5)

Coinbase415be87aae8118…4cdbe401cba8f4

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

e0c2b109716722…a26af228a21b78

8 in → 1 out294.1922 XPM1.20 KB

AdJxRmkM…FWQQKYWV

f51b9c70bd0cb8…ee7bcfa1f3a1c3

1 in → 2 out7671.9827 XPM226 B

AbZymyRQ…YZm38rjw AbscLdQE…UqKuJwhj

43b8d8e46beea7…651c90452277e5

1 in → 2 out1.1423 XPM226 B

AL86cz8Y…kKfWsz7k AVZut3KF…xVKwSpMe

da6d9f972cc651…fd3cefa705e70e

2 in → 2 out1.0571 XPM371 B

AYCgz5yi…Y8D9ahsk Abs1CTRR…uk6ieBYF

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.

1.006 × 10⁹⁹(100-digit number)

10062965603527651160…37078112177252362239

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

1.006 × 10⁹⁹(100-digit number)

10062965603527651160…37078112177252362239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.006 × 10⁹⁹(100-digit number)

10062965603527651160…37078112177252362241

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

2.012 × 10⁹⁹(100-digit number)

20125931207055302321…74156224354504724479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.012 × 10⁹⁹(100-digit number)

20125931207055302321…74156224354504724481

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

4.025 × 10⁹⁹(100-digit number)

40251862414110604643…48312448709009448959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.025 × 10⁹⁹(100-digit number)

40251862414110604643…48312448709009448961

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

8.050 × 10⁹⁹(100-digit number)

80503724828221209286…96624897418018897919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.050 × 10⁹⁹(100-digit number)

80503724828221209286…96624897418018897921

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

1.610 × 10¹⁰⁰(101-digit number)

16100744965644241857…93249794836037795839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.610 × 10¹⁰⁰(101-digit number)

16100744965644241857…93249794836037795841

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