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Block #668,898

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/8/2014, 1:35:05 PM Β· Difficulty 10.9637 Β· 6,157,948 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b1d50fdfc1641fe29e88f51c83dab6a80bcf9641e05635b53c19ee7690cce22f
View on Chainz β†—

Height

#668,898

Difficulty

10.963685

Transactions

2

Size

433 B

Version

2

Bits

0af6b415

Nonce

487,363,428

Timestamp

8/8/2014, 1:35:05 PM

Confirmations

6,157,948

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e9ff17a584a58f3540df29ae4c1a5d0250e2beb19f8349707b5ca508d2f5e145
Transactions (2)
Coinbase11fcf3762b4d0a…5df6b8fe3a76f5
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
fe9fdc86b69c63…85d75cc59ee37f
1 in β†’ 2 out2.2208 XPM226 B
AeKNrjNj…1NEq95TaAcpfxAE5…LCaYgJcv
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.

9.722 Γ— 10⁹⁢(97-digit number)
97224213070229251301…23144807098923174399
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
9.722 Γ— 10⁹⁢(97-digit number)
97224213070229251301…23144807098923174399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.722 Γ— 10⁹⁢(97-digit number)
97224213070229251301…23144807098923174401
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
1.944 Γ— 10⁹⁷(98-digit number)
19444842614045850260…46289614197846348799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.944 Γ— 10⁹⁷(98-digit number)
19444842614045850260…46289614197846348801
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
3.888 Γ— 10⁹⁷(98-digit number)
38889685228091700520…92579228395692697599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.888 Γ— 10⁹⁷(98-digit number)
38889685228091700520…92579228395692697601
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
7.777 Γ— 10⁹⁷(98-digit number)
77779370456183401041…85158456791385395199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.777 Γ— 10⁹⁷(98-digit number)
77779370456183401041…85158456791385395201
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
1.555 Γ— 10⁹⁸(99-digit number)
15555874091236680208…70316913582770790399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.555 Γ— 10⁹⁸(99-digit number)
15555874091236680208…70316913582770790401
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:57,858,934 XPMΒ·at block #6,826,845 Β· updates every 60s
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