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Block #3,003,624

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2019, 1:37:17 PM Β· Difficulty 11.2090 Β· 3,837,191 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6779064e4269b4765108af988fa84edfacbf0ed35df2319a25ff35fd37a15247
View on Chainz β†—

Height

#3,003,624

Difficulty

11.208972

Transactions

1

Size

201 B

Version

2

Bits

0b357f2c

Nonce

185,359,411

Timestamp

1/10/2019, 1:37:17 PM

Confirmations

3,837,191

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

261f41e6e4ff974c349b5d01db686851d1ce4442e203c69cd167453d28f4cf30
Transactions (1)
Coinbase261f41e6e4ff97…67453d28f4cf30
1 in β†’ 1 out7.9500 XPM110 B
AUMQRepm…tAfKmdW1
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.

3.136 Γ— 10⁹⁢(97-digit number)
31362515750646972056…48729575732331256319
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
3.136 Γ— 10⁹⁢(97-digit number)
31362515750646972056…48729575732331256319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.136 Γ— 10⁹⁢(97-digit number)
31362515750646972056…48729575732331256321
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
6.272 Γ— 10⁹⁢(97-digit number)
62725031501293944112…97459151464662512639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.272 Γ— 10⁹⁢(97-digit number)
62725031501293944112…97459151464662512641
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
1.254 Γ— 10⁹⁷(98-digit number)
12545006300258788822…94918302929325025279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.254 Γ— 10⁹⁷(98-digit number)
12545006300258788822…94918302929325025281
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
2.509 Γ— 10⁹⁷(98-digit number)
25090012600517577645…89836605858650050559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.509 Γ— 10⁹⁷(98-digit number)
25090012600517577645…89836605858650050561
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
5.018 Γ— 10⁹⁷(98-digit number)
50180025201035155290…79673211717300101119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.018 Γ— 10⁹⁷(98-digit number)
50180025201035155290…79673211717300101121
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
1.003 Γ— 10⁹⁸(99-digit number)
10036005040207031058…59346423434600202239
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:57,970,871 XPMΒ·at block #6,840,814 Β· updates every 60s
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