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Block #3,005,664

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/12/2019, 12:40:00 AM Β· Difficulty 11.1991 Β· 3,834,010 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6536727ada432ec07cc2257366b784a4ca10a749c6982a95681e5069e5383228
View on Chainz β†—

Height

#3,005,664

Difficulty

11.199051

Transactions

1

Size

199 B

Version

2

Bits

0b32f4fa

Nonce

1,165,731,014

Timestamp

1/12/2019, 12:40:00 AM

Confirmations

3,834,010

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

a2e83b79b5aadc8aac492de76864aca1cca47b92f33d25de379772ab4ce08638
Transactions (1)
Coinbasea2e83b79b5aadc…9772ab4ce08638
1 in β†’ 1 out7.9600 XPM109 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.

2.112 Γ— 10⁹⁡(96-digit number)
21127455876345425915…01878138679850731519
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
2.112 Γ— 10⁹⁡(96-digit number)
21127455876345425915…01878138679850731519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.112 Γ— 10⁹⁡(96-digit number)
21127455876345425915…01878138679850731521
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
4.225 Γ— 10⁹⁡(96-digit number)
42254911752690851831…03756277359701463039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.225 Γ— 10⁹⁡(96-digit number)
42254911752690851831…03756277359701463041
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
8.450 Γ— 10⁹⁡(96-digit number)
84509823505381703662…07512554719402926079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.450 Γ— 10⁹⁡(96-digit number)
84509823505381703662…07512554719402926081
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
1.690 Γ— 10⁹⁢(97-digit number)
16901964701076340732…15025109438805852159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.690 Γ— 10⁹⁢(97-digit number)
16901964701076340732…15025109438805852161
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
3.380 Γ— 10⁹⁢(97-digit number)
33803929402152681464…30050218877611704319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.380 Γ— 10⁹⁢(97-digit number)
33803929402152681464…30050218877611704321
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
6.760 Γ— 10⁹⁢(97-digit number)
67607858804305362929…60100437755223408639
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:57,961,681 XPMΒ·at block #6,839,673 Β· updates every 60s
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