Block #1,073,970

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2015, 5:55:04 PM · Difficulty 10.7418 · 5,724,972 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82438d4f14037ce22e33ba5b3e3c2e5a9cbc707a8ee795212dee4dedccdec452

View on Chainz ↗

Height

#1,073,970

Difficulty

10.741757

Transactions

Size

660 B

Version

Bits

0abde3c7

Nonce

351,188,276

Timestamp

5/24/2015, 5:55:04 PM

Confirmations

5,724,972

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

013ad3cca93f45ac624338c5319a89f9d1b76314fdb80a19a79da36a68ed65bd

Transactions (3)

Coinbase52067fd22618f5…548912ea67b950

1 in → 1 out8.6700 XPM116 B

ANSXnLY2…Sd25TjkD

51a2ab06286f6c…1996c66702133e

1 in → 2 out7.5581 XPM227 B

AGVCqsom…3P5bLW7b AHmcchxr…vBbydp5n

82f45c9a090540…e3a5544d65426a

1 in → 2 out5.7836 XPM227 B

AUQTH1Tx…T3nDKPgk Ae7YXEyn…hnSYZsCr

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.

6.695 × 10⁹⁴(95-digit number)

66956394868590883507…47196478774802860359

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

6.695 × 10⁹⁴(95-digit number)

66956394868590883507…47196478774802860359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.695 × 10⁹⁴(95-digit number)

66956394868590883507…47196478774802860361

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

1.339 × 10⁹⁵(96-digit number)

13391278973718176701…94392957549605720719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.339 × 10⁹⁵(96-digit number)

13391278973718176701…94392957549605720721

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

2.678 × 10⁹⁵(96-digit number)

26782557947436353403…88785915099211441439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.678 × 10⁹⁵(96-digit number)

26782557947436353403…88785915099211441441

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

5.356 × 10⁹⁵(96-digit number)

53565115894872706806…77571830198422882879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.356 × 10⁹⁵(96-digit number)

53565115894872706806…77571830198422882881

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

1.071 × 10⁹⁶(97-digit number)

10713023178974541361…55143660396845765759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.071 × 10⁹⁶(97-digit number)

10713023178974541361…55143660396845765761

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