Block #609,334

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/1/2014, 3:57:58 AM · Difficulty 10.9117 · 6,187,038 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9a0ee31b9aef8795ed61a17a3c64b3cba3e1144bfc67b7fc6f94f3d7a2836213

View on Chainz ↗

Height

#609,334

Difficulty

10.911699

Transactions

Size

1.55 KB

Version

Bits

0ae9651a

Nonce

241,259,577

Timestamp

7/1/2014, 3:57:58 AM

Confirmations

6,187,038

Mined by

⛏️ 6LAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1c87fa85b792f6906067d56e8971faa6040551a091035db703bf9699c01b7a2a

Transactions (4)

Coinbase7631a0b10857a2…66bbe3fa9f7836

1 in → 18 out8.3900 XPM675 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn AGKhfQo2…h7fBXLX6

ede966f94139b2…b7187f77257530

1 in → 2 out8.3700 XPM226 B

AcpypRxu…cnTctSuJ AdMm8r3r…rbJShgSr

bc7e5a2aa799d2…9e3992e1af3f10

2 in → 2 out16.8100 XPM373 B

AHj8zdgn…97aJ9bxZ AHdkjDnS…SYJhF91Y

da9fc7850a2015…806c785a90fb4d

1 in → 2 out8.3700 XPM225 B

ANQcLuxb…h5eS9Jmr Ab4B7gLw…BfczdVYc

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.

1.176 × 10⁹⁸(99-digit number)

11768760001332996209…16904084569429923199

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

1.176 × 10⁹⁸(99-digit number)

11768760001332996209…16904084569429923199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.176 × 10⁹⁸(99-digit number)

11768760001332996209…16904084569429923201

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

2.353 × 10⁹⁸(99-digit number)

23537520002665992418…33808169138859846399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.353 × 10⁹⁸(99-digit number)

23537520002665992418…33808169138859846401

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

4.707 × 10⁹⁸(99-digit number)

47075040005331984836…67616338277719692799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.707 × 10⁹⁸(99-digit number)

47075040005331984836…67616338277719692801

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

9.415 × 10⁹⁸(99-digit number)

94150080010663969672…35232676555439385599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.415 × 10⁹⁸(99-digit number)

94150080010663969672…35232676555439385601

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

1.883 × 10⁹⁹(100-digit number)

18830016002132793934…70465353110878771199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.883 × 10⁹⁹(100-digit number)

18830016002132793934…70465353110878771201

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