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Block #2,279,476

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2017, 4:28:03 PM Β· Difficulty 10.9559 Β· 4,553,550 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0e7dc72c074f6eb0708aba2dab53de03c04f2d5f083da8f787e19822bdd2973e
View on Chainz β†—

Height

#2,279,476

Difficulty

10.955887

Transactions

2

Size

426 B

Version

2

Bits

0af4b506

Nonce

422,280,323

Timestamp

9/2/2017, 4:28:03 PM

Confirmations

4,553,550

Mined by

⛏️ P2SHAYAyWesEqbYDU8p7rDYJn1gFZkhoSdf6Hr

Merkle Root

1e856994c5a2321ffd59bd78f5a86aac94687770f2b373dd2c73ba495f5b196b
Transactions (2)
Coinbase208304145094df…4988702d42abd8
1 in β†’ 1 out8.3300 XPM110 B
AYAyWesE…hoSdf6Hr
7ffc235c48ce14…b2829e1ff0e33c
1 in β†’ 2 out1975.9508 XPM226 B
Ae7gNjP6…qJe42JksAKQmMBD1…FvefJGwc
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.

5.517 Γ— 10⁹⁴(95-digit number)
55179927445840019497…04584175991252840799
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
5.517 Γ— 10⁹⁴(95-digit number)
55179927445840019497…04584175991252840799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.517 Γ— 10⁹⁴(95-digit number)
55179927445840019497…04584175991252840801
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
1.103 Γ— 10⁹⁡(96-digit number)
11035985489168003899…09168351982505681599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.103 Γ— 10⁹⁡(96-digit number)
11035985489168003899…09168351982505681601
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
2.207 Γ— 10⁹⁡(96-digit number)
22071970978336007799…18336703965011363199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.207 Γ— 10⁹⁡(96-digit number)
22071970978336007799…18336703965011363201
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
4.414 Γ— 10⁹⁡(96-digit number)
44143941956672015598…36673407930022726399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.414 Γ— 10⁹⁡(96-digit number)
44143941956672015598…36673407930022726401
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
8.828 Γ— 10⁹⁡(96-digit number)
88287883913344031196…73346815860045452799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.828 Γ— 10⁹⁡(96-digit number)
88287883913344031196…73346815860045452801
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
1.765 Γ— 10⁹⁢(97-digit number)
17657576782668806239…46693631720090905599
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:57,908,384 XPMΒ·at block #6,833,025 Β· updates every 60s
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