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Block #3,141,275

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/16/2019, 2:41:13 AM Β· Difficulty 11.3178 Β· 3,701,028 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5ec81c03f0a438b948a3dfb9095d370a7aaba345505d37f4cec6842728352864
View on Chainz β†—

Height

#3,141,275

Difficulty

11.317814

Transactions

2

Size

723 B

Version

2

Bits

0b515c4a

Nonce

2,126,485,492

Timestamp

4/16/2019, 2:41:13 AM

Confirmations

3,701,028

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

27c5fb121f4cbd01d6e306fa0829c98e7bfa252e0f809327c4fb28e5b2b62866
Transactions (2)
Coinbase879949afdb1526…cd0478aad071f3
1 in β†’ 1 out7.8000 XPM110 B
AbXwmGxD…4XXYP765
7c8c8b1462ddc4…2c506e5f3083ae
3 in β†’ 2 out142.6705 XPM522 B
Ab9ymyu2…yh7Uu4SLAevAFhdo…mGS3Nx7j
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.637 Γ— 10⁹⁢(97-digit number)
36375882900443764234…28461397524246527999
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.637 Γ— 10⁹⁢(97-digit number)
36375882900443764234…28461397524246527999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.637 Γ— 10⁹⁢(97-digit number)
36375882900443764234…28461397524246528001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
7.275 Γ— 10⁹⁢(97-digit number)
72751765800887528469…56922795048493055999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.275 Γ— 10⁹⁢(97-digit number)
72751765800887528469…56922795048493056001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.455 Γ— 10⁹⁷(98-digit number)
14550353160177505693…13845590096986111999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.455 Γ— 10⁹⁷(98-digit number)
14550353160177505693…13845590096986112001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.910 Γ— 10⁹⁷(98-digit number)
29100706320355011387…27691180193972223999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.910 Γ— 10⁹⁷(98-digit number)
29100706320355011387…27691180193972224001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
5.820 Γ— 10⁹⁷(98-digit number)
58201412640710022775…55382360387944447999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.820 Γ— 10⁹⁷(98-digit number)
58201412640710022775…55382360387944448001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁸(99-digit number)
11640282528142004555…10764720775888895999
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,982,829 XPMΒ·at block #6,842,302 Β· updates every 60s
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