Block #2,051,947

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2017, 4:48:01 PM · Difficulty 10.7288 · 4,760,745 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

02053cebd57025511ca3cbca6415f76893832664375081182c2556b793c88dfd

View on Chainz ↗

Height

#2,051,947

Difficulty

10.728770

Transactions

Size

5.13 KB

Version

Bits

0aba90a9

Nonce

1,204,939,144

Timestamp

4/3/2017, 4:48:01 PM

Confirmations

4,760,745

Mined by

⛏️ P2SHASYCtQwJuuiRMtGsBT1Ww4tXCPfSkiNnX3

Merkle Root

b84a1332bd18b90e1339d1c97d34f7ecbe7c57e15d7a8fe9a8d03bc3da352052

Transactions (5)

Coinbase7420a9a9e2ee66…24b5c5449e7f00

1 in → 1 out8.7500 XPM110 B

ASYCtQwJ…fSkiNnX3

8bc86bb595a600…180d883d67fabd

3 in → 2 out4028.3862 XPM520 B

AcVxnTXh…gD7QBVEe AV7gdD8Z…SdC5DKxQ

5c7d033071476f…c161e1ced2db73

27 in → 2 out405.1490 XPM3.98 KB

AaKQyHUt…ZKgoa2oY ANka8hPb…YBmx1L35

2a2eed768c8ac5…3e8444af07bf87

1 in → 2 out11862.7828 XPM227 B

AKSKX6NC…MWXfsh3G AMxcrnTm…ddJs9Erb

cc79ca10addbb1…040425bef78f6d

1 in → 2 out6802.8828 XPM225 B

AVBcMJ7V…aT9j2Mkq AJHwYEqX…zoMyGsRg

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.

1.372 × 10⁹⁴(95-digit number)

13724624547225544249…86714631459625176639

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

1.372 × 10⁹⁴(95-digit number)

13724624547225544249…86714631459625176639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.372 × 10⁹⁴(95-digit number)

13724624547225544249…86714631459625176641

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

2.744 × 10⁹⁴(95-digit number)

27449249094451088498…73429262919250353279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.744 × 10⁹⁴(95-digit number)

27449249094451088498…73429262919250353281

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

5.489 × 10⁹⁴(95-digit number)

54898498188902176996…46858525838500706559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.489 × 10⁹⁴(95-digit number)

54898498188902176996…46858525838500706561

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

1.097 × 10⁹⁵(96-digit number)

10979699637780435399…93717051677001413119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.097 × 10⁹⁵(96-digit number)

10979699637780435399…93717051677001413121

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

2.195 × 10⁹⁵(96-digit number)

21959399275560870798…87434103354002826239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.195 × 10⁹⁵(96-digit number)

21959399275560870798…87434103354002826241

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 #2,051,947

Cookie Preferences