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Block #858,586

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/18/2014, 6:00:46 PM Β· Difficulty 10.9666 Β· 5,985,920 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c87758a62198fd8a9d1c00d3066a3e235b814c8e78cc0e158025d27896a4b299
View on Chainz β†—

Height

#858,586

Difficulty

10.966552

Transactions

2

Size

433 B

Version

2

Bits

0af76fef

Nonce

102,759,668

Timestamp

12/18/2014, 6:00:46 PM

Confirmations

5,985,920

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5535e2d08dd07bef5901f7f3412750f39c25b14480ca0aeebb80925b522a1f7b
Transactions (2)
Coinbase968208ba662330…e59bb3abf246a1
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
4463177979f64f…57c77fe980ec7c
1 in β†’ 2 out0.0272 XPM226 B
AQwSwzWo…Aph3kycUARS9tRBt…PeCZ27ZP
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.

1.008 Γ— 10⁹⁷(98-digit number)
10080700655676402121…57120279305177459199
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
1.008 Γ— 10⁹⁷(98-digit number)
10080700655676402121…57120279305177459199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.008 Γ— 10⁹⁷(98-digit number)
10080700655676402121…57120279305177459201
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
2.016 Γ— 10⁹⁷(98-digit number)
20161401311352804242…14240558610354918399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.016 Γ— 10⁹⁷(98-digit number)
20161401311352804242…14240558610354918401
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
4.032 Γ— 10⁹⁷(98-digit number)
40322802622705608485…28481117220709836799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.032 Γ— 10⁹⁷(98-digit number)
40322802622705608485…28481117220709836801
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
8.064 Γ— 10⁹⁷(98-digit number)
80645605245411216971…56962234441419673599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.064 Γ— 10⁹⁷(98-digit number)
80645605245411216971…56962234441419673601
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
1.612 Γ— 10⁹⁸(99-digit number)
16129121049082243394…13924468882839347199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.612 Γ— 10⁹⁸(99-digit number)
16129121049082243394…13924468882839347201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 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
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 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:58,000,446 XPMΒ·at block #6,844,505 Β· updates every 60s
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