Block #841,091

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/5/2014, 3:28:53 PM · Difficulty 10.9741 · 5,986,253 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2dc0d3884dd2e455d8a23f72f2bc37339ba4b850035a9966b74ee40935396a8

View on Chainz ↗

Height

#841,091

Difficulty

10.974078

Transactions

Size

1.09 KB

Version

Bits

0af95d33

Nonce

183,500,605

Timestamp

12/5/2014, 3:28:53 PM

Confirmations

5,986,253

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

13ab50d5328c8f6b4e1abce2b32d319aa70b1e742912c03e31fd1d1640879492

Transactions (5)

Coinbasecb95c58fd09b4e…711648b13a7988

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

43d6fa40b89370…02ca18e4438c9c

1 in → 2 out0.1053 XPM226 B

AQf6pY9S…6o1MeRsp AWLH3ZDN…sDccyL7z

dfc34742b5b34e…7dbe92b3ca75ac

1 in → 2 out0.0736 XPM226 B

AJ4f5F2C…SpfMNrWk AcMvu8Xe…fcwxKJps

5dff4e91468df9…d9cc3a707690bc

1 in → 2 out0.0474 XPM226 B

AdxWVTbM…8SfuSFxu AWg7Ee38…ps4pLZut

2aacde8cf28420…9d373225d2fb11

1 in → 2 out0.0941 XPM227 B

AcFvjmCp…GGSt2NQR AR827L4w…ss8i9J4R

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.

3.178 × 10⁹⁹(100-digit number)

31786729201774684169…15851861888995819519

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

3.178 × 10⁹⁹(100-digit number)

31786729201774684169…15851861888995819519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.178 × 10⁹⁹(100-digit number)

31786729201774684169…15851861888995819521

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

6.357 × 10⁹⁹(100-digit number)

63573458403549368339…31703723777991639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.357 × 10⁹⁹(100-digit number)

63573458403549368339…31703723777991639041

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

1.271 × 10¹⁰⁰(101-digit number)

12714691680709873667…63407447555983278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.271 × 10¹⁰⁰(101-digit number)

12714691680709873667…63407447555983278081

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

2.542 × 10¹⁰⁰(101-digit number)

25429383361419747335…26814895111966556159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.542 × 10¹⁰⁰(101-digit number)

25429383361419747335…26814895111966556161

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

5.085 × 10¹⁰⁰(101-digit number)

50858766722839494671…53629790223933112319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.085 × 10¹⁰⁰(101-digit number)

50858766722839494671…53629790223933112321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.017 × 10¹⁰¹(102-digit number)

10171753344567898934…07259580447866224639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #841,091

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