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Block #671,287

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/10/2014, 4:45:37 AM Β· Difficulty 10.9640 Β· 6,134,927 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dbcdbd3a571c46f7de312a31b1bdf5178ed2561563892132d98d94f33ef6ab2e
View on Chainz β†—

Height

#671,287

Difficulty

10.964044

Transactions

1

Size

207 B

Version

2

Bits

0af6cb98

Nonce

413,826,665

Timestamp

8/10/2014, 4:45:37 AM

Confirmations

6,134,927

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

98243367fab3f2afd536f0a6ab0585472a227de054832e91e71bb8d345e7b4c1
Transactions (1)
Coinbase98243367fab3f2…1bb8d345e7b4c1
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

3.936 Γ— 10⁹⁢(97-digit number)
39369891643161267806…52703258788764181439
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
3.936 Γ— 10⁹⁢(97-digit number)
39369891643161267806…52703258788764181439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.936 Γ— 10⁹⁢(97-digit number)
39369891643161267806…52703258788764181441
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
7.873 Γ— 10⁹⁢(97-digit number)
78739783286322535613…05406517577528362879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.873 Γ— 10⁹⁢(97-digit number)
78739783286322535613…05406517577528362881
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
1.574 Γ— 10⁹⁷(98-digit number)
15747956657264507122…10813035155056725759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.574 Γ— 10⁹⁷(98-digit number)
15747956657264507122…10813035155056725761
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
3.149 Γ— 10⁹⁷(98-digit number)
31495913314529014245…21626070310113451519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.149 Γ— 10⁹⁷(98-digit number)
31495913314529014245…21626070310113451521
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
6.299 Γ— 10⁹⁷(98-digit number)
62991826629058028490…43252140620226903039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.299 Γ— 10⁹⁷(98-digit number)
62991826629058028490…43252140620226903041
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
1.259 Γ— 10⁹⁸(99-digit number)
12598365325811605698…86504281240453806079
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:57,693,792 XPMΒ·at block #6,806,213 Β· updates every 60s
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