Block #870,809

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2014, 4:57:44 PM · Difficulty 10.9621 · 5,946,585 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f1de359255bfe6cd8e56de7d40cbf265e0faa75500f2187583b9498ff7206f31

View on Chainz ↗

Height

#870,809

Difficulty

10.962148

Transactions

Size

1.22 KB

Version

Bits

0af64f5a

Nonce

702,353,089

Timestamp

12/27/2014, 4:57:44 PM

Confirmations

5,946,585

Mined by

⛏️ P2SHAYu4e8J5TH9r9S9ReZLwxuapi64LPfG8PR

Merkle Root

128e78339520a5b660f73cf33aa20988ca9ab247f138211e5af95cd3a583be9c

Transactions (5)

Coinbase588aad77fc764d…82c1938d1ab6e4

1 in → 1 out8.3500 XPM109 B

AYu4e8J5…4LPfG8PR

97804e79c64098…d99c767dd7e3e6

1 in → 2 out7.2251 XPM227 B

AHRoBSh4…BSVTQ36Q AN6sGAkX…zt4RktCr

ba9c9fea196d97…d5b393e94e882d

1 in → 2 out6.0607 XPM226 B

ALcPi2tw…YR278v9L ALP6szJY…eEPSo5sX

4cf4cd45ea8ba8…06db3847677346

1 in → 2 out5.3008 XPM226 B

Ae7YXEyn…hnSYZsCr AeUtXSAX…DpxeeJFu

be6c54061245f2…fcaa1007c399a1

2 in → 2 out5.0358 XPM375 B

AKZMVBtp…Lh7ZP1EZ AbDH16rg…w2PMg7mN

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.

5.430 × 10⁹⁴(95-digit number)

54304866382288627926…64672912193541031679

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

5.430 × 10⁹⁴(95-digit number)

54304866382288627926…64672912193541031679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.430 × 10⁹⁴(95-digit number)

54304866382288627926…64672912193541031681

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

1.086 × 10⁹⁵(96-digit number)

10860973276457725585…29345824387082063359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.086 × 10⁹⁵(96-digit number)

10860973276457725585…29345824387082063361

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

2.172 × 10⁹⁵(96-digit number)

21721946552915451170…58691648774164126719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.172 × 10⁹⁵(96-digit number)

21721946552915451170…58691648774164126721

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

4.344 × 10⁹⁵(96-digit number)

43443893105830902341…17383297548328253439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.344 × 10⁹⁵(96-digit number)

43443893105830902341…17383297548328253441

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

8.688 × 10⁹⁵(96-digit number)

86887786211661804683…34766595096656506879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.688 × 10⁹⁵(96-digit number)

86887786211661804683…34766595096656506881

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 #870,809

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