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Block #2,946,017

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2018, 2:38:51 PM Β· Difficulty 11.3951 Β· 3,890,862 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2661d69a00e8ceca973de57acc78a62256b0b256f632c5a0e931fce72aa6bccd
View on Chainz β†—

Height

#2,946,017

Difficulty

11.395149

Transactions

1

Size

201 B

Version

2

Bits

0b652883

Nonce

1,769,869,103

Timestamp

11/30/2018, 2:38:51 PM

Confirmations

3,890,862

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

e252bd0bc68d371700af17316ba1b8d16bfb18aecc6f97c6562d98d2c1bdbdb4
Transactions (1)
Coinbasee252bd0bc68d37…2d98d2c1bdbdb4
1 in β†’ 1 out7.6900 XPM110 B
AUhjokok…k5m93PZR
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.

9.530 Γ— 10⁹⁢(97-digit number)
95300951650815185953…63197502848039444479
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
9.530 Γ— 10⁹⁢(97-digit number)
95300951650815185953…63197502848039444479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.530 Γ— 10⁹⁢(97-digit number)
95300951650815185953…63197502848039444481
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
1.906 Γ— 10⁹⁷(98-digit number)
19060190330163037190…26395005696078888959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.906 Γ— 10⁹⁷(98-digit number)
19060190330163037190…26395005696078888961
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
3.812 Γ— 10⁹⁷(98-digit number)
38120380660326074381…52790011392157777919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.812 Γ— 10⁹⁷(98-digit number)
38120380660326074381…52790011392157777921
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
7.624 Γ— 10⁹⁷(98-digit number)
76240761320652148762…05580022784315555839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.624 Γ— 10⁹⁷(98-digit number)
76240761320652148762…05580022784315555841
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
1.524 Γ— 10⁹⁸(99-digit number)
15248152264130429752…11160045568631111679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.524 Γ— 10⁹⁸(99-digit number)
15248152264130429752…11160045568631111681
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
3.049 Γ— 10⁹⁸(99-digit number)
30496304528260859505…22320091137262223359
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:57,939,323 XPMΒ·at block #6,836,878 Β· updates every 60s
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