Block #1,061,884

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2015, 11:57:20 AM · Difficulty 10.7305 · 5,780,546 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

78b39e4c279683a316d984bb7f8d8c20d1bae95b966cffa63baaa6f811de8103

View on Chainz ↗

Height

#1,061,884

Difficulty

10.730495

Transactions

Size

3.74 KB

Version

Bits

0abb01b8

Nonce

1,664,462,707

Timestamp

5/16/2015, 11:57:20 AM

Confirmations

5,780,546

Mined by

⛏️ P2SHAYpRYZtTf4wHBovFakjrV8ArkYtf3zvLMK

Merkle Root

259d77315b81596d0c33c5ca1e75bcebcc86434baddd4cf728490c92d37cabef

Transactions (2)

Coinbase86b2d96b6aef99…0e9b5e352239d0

1 in → 1 out8.7100 XPM109 B

AYpRYZtT…tf3zvLMK

4038dfdfb93dbf…e4cbacf34dcdca

24 in → 2 out370.0161 XPM3.54 KB

ALRuXegM…qhkfJpvU AWX9DWsj…UucVdngh

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.

1.118 × 10⁹⁵(96-digit number)

11183628578656372528…12256939103598875999

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

1.118 × 10⁹⁵(96-digit number)

11183628578656372528…12256939103598875999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.118 × 10⁹⁵(96-digit number)

11183628578656372528…12256939103598876001

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

2.236 × 10⁹⁵(96-digit number)

22367257157312745057…24513878207197751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.236 × 10⁹⁵(96-digit number)

22367257157312745057…24513878207197752001

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

4.473 × 10⁹⁵(96-digit number)

44734514314625490114…49027756414395503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.473 × 10⁹⁵(96-digit number)

44734514314625490114…49027756414395504001

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

8.946 × 10⁹⁵(96-digit number)

89469028629250980229…98055512828791007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.946 × 10⁹⁵(96-digit number)

89469028629250980229…98055512828791008001

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

1.789 × 10⁹⁶(97-digit number)

17893805725850196045…96111025657582015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.789 × 10⁹⁶(97-digit number)

17893805725850196045…96111025657582016001

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 #1,061,884

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