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Block #672,231

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/10/2014, 7:18:59 PM Β· Difficulty 10.9646 Β· 6,126,599 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e0557721b3c7313a2769953fd4e935d2c999d5e5b62e6e22dae9bda0287335af
View on Chainz β†—

Height

#672,231

Difficulty

10.964569

Transactions

2

Size

1.00 KB

Version

2

Bits

0af6edfa

Nonce

470,446,354

Timestamp

8/10/2014, 7:18:59 PM

Confirmations

6,126,599

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b999fbe71f733cf578fea7eeee37cac90078334832f6b698e68ed16c4fee7317
Transactions (2)
Coinbase2301b3c24e2714…46fe5b65218ad3
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
3f21b09acf044b…5f4f2ac5c2701c
5 in β†’ 2 out10.0337 XPM820 B
AZFyR8n4…Xiiavx12AFudLPUx…GvrQejgU
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.

3.194 Γ— 10⁹⁷(98-digit number)
31942661960585296361…39732927200116285439
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
3.194 Γ— 10⁹⁷(98-digit number)
31942661960585296361…39732927200116285439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.194 Γ— 10⁹⁷(98-digit number)
31942661960585296361…39732927200116285441
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
6.388 Γ— 10⁹⁷(98-digit number)
63885323921170592722…79465854400232570879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.388 Γ— 10⁹⁷(98-digit number)
63885323921170592722…79465854400232570881
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
1.277 Γ— 10⁹⁸(99-digit number)
12777064784234118544…58931708800465141759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.277 Γ— 10⁹⁸(99-digit number)
12777064784234118544…58931708800465141761
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
2.555 Γ— 10⁹⁸(99-digit number)
25554129568468237088…17863417600930283519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.555 Γ— 10⁹⁸(99-digit number)
25554129568468237088…17863417600930283521
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
5.110 Γ— 10⁹⁸(99-digit number)
51108259136936474177…35726835201860567039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.110 Γ— 10⁹⁸(99-digit number)
51108259136936474177…35726835201860567041
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
1.022 Γ— 10⁹⁹(100-digit number)
10221651827387294835…71453670403721134079
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:57,634,670 XPMΒ·at block #6,798,829 Β· updates every 60s
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