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Block #2,885,217

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/17/2018, 4:32:43 PM Β· Difficulty 11.6261 Β· 3,959,671 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
34eb6bb448d04bd6b46f6f27762e6e65ce7c86f37119de00d2f6f5f80595f716
View on Chainz β†—

Height

#2,885,217

Difficulty

11.626051

Transactions

1

Size

200 B

Version

2

Bits

0ba044e9

Nonce

1,732,049,963

Timestamp

10/17/2018, 4:32:43 PM

Confirmations

3,959,671

Mined by

⛏️ P2SHAKPStKZUHokzwhJBuwRzSJH1CKpbsGue9L

Merkle Root

b15d4883ebfc96fe51e3d02ac3f8b54a75169b45c757cf32ba077a6ccd49268d
Transactions (1)
Coinbaseb15d4883ebfc96…077a6ccd49268d
1 in β†’ 1 out7.3900 XPM110 B
AKPStKZU…pbsGue9L
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.

1.065 Γ— 10⁹⁴(95-digit number)
10652684658087078347…69608211618729717759
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
1.065 Γ— 10⁹⁴(95-digit number)
10652684658087078347…69608211618729717759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.065 Γ— 10⁹⁴(95-digit number)
10652684658087078347…69608211618729717761
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
2.130 Γ— 10⁹⁴(95-digit number)
21305369316174156695…39216423237459435519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.130 Γ— 10⁹⁴(95-digit number)
21305369316174156695…39216423237459435521
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
4.261 Γ— 10⁹⁴(95-digit number)
42610738632348313391…78432846474918871039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.261 Γ— 10⁹⁴(95-digit number)
42610738632348313391…78432846474918871041
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
8.522 Γ— 10⁹⁴(95-digit number)
85221477264696626783…56865692949837742079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.522 Γ— 10⁹⁴(95-digit number)
85221477264696626783…56865692949837742081
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
1.704 Γ— 10⁹⁡(96-digit number)
17044295452939325356…13731385899675484159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.704 Γ— 10⁹⁡(96-digit number)
17044295452939325356…13731385899675484161
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
3.408 Γ— 10⁹⁡(96-digit number)
34088590905878650713…27462771799350968319
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:58,003,519 XPMΒ·at block #6,844,887 Β· updates every 60s
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