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Block #667,722

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2014, 7:35:01 PM Β· Difficulty 10.9630 Β· 6,146,145 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5899adfce7d9bea6598a9f845275b03739156ee932e3c6eae67ccc250d147a24
View on Chainz β†—

Height

#667,722

Difficulty

10.962952

Transactions

2

Size

432 B

Version

2

Bits

0af6840b

Nonce

583,733,979

Timestamp

8/7/2014, 7:35:01 PM

Confirmations

6,146,145

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d53b17f751db958a566b7751690a240c8e535a12f78f8d70a5c3306d4e224e99
Transactions (2)
Coinbase575a63e0076649…f13f2385e6153d
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
57a1a89428fa42…c94a6f28377b5b
1 in β†’ 2 out2.2229 XPM226 B
AeKNrjNj…1NEq95TaATz1Sryu…PWZHWKYx
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.

1.739 Γ— 10⁹⁡(96-digit number)
17396241540186167583…25563840389907349759
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
1.739 Γ— 10⁹⁡(96-digit number)
17396241540186167583…25563840389907349759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.739 Γ— 10⁹⁡(96-digit number)
17396241540186167583…25563840389907349761
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
3.479 Γ— 10⁹⁡(96-digit number)
34792483080372335166…51127680779814699519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.479 Γ— 10⁹⁡(96-digit number)
34792483080372335166…51127680779814699521
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
6.958 Γ— 10⁹⁡(96-digit number)
69584966160744670333…02255361559629399039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.958 Γ— 10⁹⁡(96-digit number)
69584966160744670333…02255361559629399041
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
1.391 Γ— 10⁹⁢(97-digit number)
13916993232148934066…04510723119258798079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.391 Γ— 10⁹⁢(97-digit number)
13916993232148934066…04510723119258798081
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
2.783 Γ— 10⁹⁢(97-digit number)
27833986464297868133…09021446238517596159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.783 Γ— 10⁹⁢(97-digit number)
27833986464297868133…09021446238517596161
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:57,755,009 XPMΒ·at block #6,813,866 Β· updates every 60s
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