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Block #2,451,911

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/1/2018, 2:45:03 AM Β· Difficulty 10.9498 Β· 4,381,827 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8f085381e043ce2362a5a42e66ec436ce14aa81f4233c2cba1c1d8285f64cc84
View on Chainz β†—

Height

#2,451,911

Difficulty

10.949813

Transactions

2

Size

427 B

Version

2

Bits

0af326f0

Nonce

115,081,269

Timestamp

1/1/2018, 2:45:03 AM

Confirmations

4,381,827

Mined by

⛏️ P2SHAFqWnzGUNNqQTfZVeakcYb3Giv9GKN7wtb

Merkle Root

5d585e5f48c1194f00c53b29ae5e85a0817cad02b68c431ec20b1912babc3c8c
Transactions (2)
Coinbase7b322916d6e552…5e10623763544f
1 in β†’ 1 out8.3400 XPM110 B
AFqWnzGU…9GKN7wtb
5d777197c3de7f…a65c3f89fab2a5
1 in β†’ 2 out754.5925 XPM226 B
AQV2cMEF…SFfb2zE5ALyhc6tF…E5eQG29x
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.

9.649 Γ— 10⁹⁷(98-digit number)
96490555886333241428…77386775771104870399
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
9.649 Γ— 10⁹⁷(98-digit number)
96490555886333241428…77386775771104870399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.649 Γ— 10⁹⁷(98-digit number)
96490555886333241428…77386775771104870401
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
1.929 Γ— 10⁹⁸(99-digit number)
19298111177266648285…54773551542209740799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.929 Γ— 10⁹⁸(99-digit number)
19298111177266648285…54773551542209740801
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
3.859 Γ— 10⁹⁸(99-digit number)
38596222354533296571…09547103084419481599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.859 Γ— 10⁹⁸(99-digit number)
38596222354533296571…09547103084419481601
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
7.719 Γ— 10⁹⁸(99-digit number)
77192444709066593142…19094206168838963199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.719 Γ— 10⁹⁸(99-digit number)
77192444709066593142…19094206168838963201
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
1.543 Γ— 10⁹⁹(100-digit number)
15438488941813318628…38188412337677926399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.543 Γ— 10⁹⁹(100-digit number)
15438488941813318628…38188412337677926401
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
3.087 Γ— 10⁹⁹(100-digit number)
30876977883626637257…76376824675355852799
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:57,914,121 XPMΒ·at block #6,833,737 Β· updates every 60s
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