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Block #1,692,212

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/28/2016, 5:02:59 AM Β· Difficulty 10.6841 Β· 5,147,362 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e5669cbdde1a56006c85a208aa0761045573cccfd99e0f06ca2408dfbab62ab8
View on Chainz β†—

Height

#1,692,212

Difficulty

10.684127

Transactions

1

Size

201 B

Version

2

Bits

0aaf22f6

Nonce

699,099,624

Timestamp

7/28/2016, 5:02:59 AM

Confirmations

5,147,362

Mined by

⛏️ P2SHASRHaiffiDYJqarW6Z7LHPtRopzpnjNfLT

Merkle Root

737e4fb6ddea32122276b06c1fe6b42c46c8b80169f116d0c589d4e892b6a5fd
Transactions (1)
Coinbase737e4fb6ddea32…89d4e892b6a5fd
1 in β†’ 1 out8.7500 XPM110 B
ASRHaiff…zpnjNfLT
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.

2.991 Γ— 10⁹⁢(97-digit number)
29919168681085995687…34099833042022131199
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
2.991 Γ— 10⁹⁢(97-digit number)
29919168681085995687…34099833042022131199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.991 Γ— 10⁹⁢(97-digit number)
29919168681085995687…34099833042022131201
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
5.983 Γ— 10⁹⁢(97-digit number)
59838337362171991374…68199666084044262399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.983 Γ— 10⁹⁢(97-digit number)
59838337362171991374…68199666084044262401
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
1.196 Γ— 10⁹⁷(98-digit number)
11967667472434398274…36399332168088524799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.196 Γ— 10⁹⁷(98-digit number)
11967667472434398274…36399332168088524801
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
2.393 Γ— 10⁹⁷(98-digit number)
23935334944868796549…72798664336177049599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.393 Γ— 10⁹⁷(98-digit number)
23935334944868796549…72798664336177049601
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
4.787 Γ— 10⁹⁷(98-digit number)
47870669889737593099…45597328672354099199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.787 Γ— 10⁹⁷(98-digit number)
47870669889737593099…45597328672354099201
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:57,960,878 XPMΒ·at block #6,839,573 Β· updates every 60s
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