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Block #667,652

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2014, 6:31:30 PM Β· Difficulty 10.9629 Β· 6,141,372 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0b5b23c639a8982967203f1fd394c4d759727d9e07586931c84c0de082aa5674
View on Chainz β†—

Height

#667,652

Difficulty

10.962908

Transactions

2

Size

581 B

Version

2

Bits

0af6811f

Nonce

133,830,462

Timestamp

8/7/2014, 6:31:30 PM

Confirmations

6,141,372

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0aa8f77d8356dec713960dfccefe2a4dfaaa847b084178aba419452a930c2f9d
Transactions (2)
Coinbase6975a05a18dc20…5fd6c5c778349c
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
903caccbcce356…6933c4bbde9e21
2 in β†’ 2 out11.0692 XPM374 B
AbCf9D8v…6KV2gwxCAZFyR8n4…Xiiavx12
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.

8.330 Γ— 10⁹⁢(97-digit number)
83300569605558943065…56936861479221446079
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
8.330 Γ— 10⁹⁢(97-digit number)
83300569605558943065…56936861479221446079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.330 Γ— 10⁹⁢(97-digit number)
83300569605558943065…56936861479221446081
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
1.666 Γ— 10⁹⁷(98-digit number)
16660113921111788613…13873722958442892159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.666 Γ— 10⁹⁷(98-digit number)
16660113921111788613…13873722958442892161
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
3.332 Γ— 10⁹⁷(98-digit number)
33320227842223577226…27747445916885784319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.332 Γ— 10⁹⁷(98-digit number)
33320227842223577226…27747445916885784321
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
6.664 Γ— 10⁹⁷(98-digit number)
66640455684447154452…55494891833771568639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.664 Γ— 10⁹⁷(98-digit number)
66640455684447154452…55494891833771568641
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
1.332 Γ— 10⁹⁸(99-digit number)
13328091136889430890…10989783667543137279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.332 Γ— 10⁹⁸(99-digit number)
13328091136889430890…10989783667543137281
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:57,716,255 XPMΒ·at block #6,809,023 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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