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Block #2,158,074

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/12/2017, 8:20:21 PM Β· Difficulty 10.9047 Β· 4,659,747 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7c02b2645229da4b1ed739d0f7287f307bfd129f0c04ad793a03ed2c1b3b0a85
View on Chainz β†—

Height

#2,158,074

Difficulty

10.904675

Transactions

2

Size

1.86 KB

Version

2

Bits

0ae798cd

Nonce

315,977,776

Timestamp

6/12/2017, 8:20:21 PM

Confirmations

4,659,747

Mined by

⛏️ P2SHAFwHQakWGSGYYcfCUSHoBq8foCYGr834m7

Merkle Root

52aca4b57b49385aa634eb75317f59b7733115e2d8e5583eb65c0c813bf28d69
Transactions (2)
Coinbase180f983ca11fc1…86a945b1c64995
1 in β†’ 1 out8.4200 XPM109 B
AFwHQakW…YGr834m7
a42c7e99eb7b8c…92098fdd04b33b
11 in β†’ 2 out628.7604 XPM1.67 KB
Ae13nBXV…Vg4cziS4ANzQV8qU…MLDu8V3P
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.

6.498 Γ— 10⁹⁡(96-digit number)
64986575223546086834…19446725234059566079
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
6.498 Γ— 10⁹⁡(96-digit number)
64986575223546086834…19446725234059566079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.498 Γ— 10⁹⁡(96-digit number)
64986575223546086834…19446725234059566081
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
1.299 Γ— 10⁹⁢(97-digit number)
12997315044709217366…38893450468119132159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.299 Γ— 10⁹⁢(97-digit number)
12997315044709217366…38893450468119132161
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
2.599 Γ— 10⁹⁢(97-digit number)
25994630089418434733…77786900936238264319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.599 Γ— 10⁹⁢(97-digit number)
25994630089418434733…77786900936238264321
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
5.198 Γ— 10⁹⁢(97-digit number)
51989260178836869467…55573801872476528639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.198 Γ— 10⁹⁢(97-digit number)
51989260178836869467…55573801872476528641
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
1.039 Γ— 10⁹⁷(98-digit number)
10397852035767373893…11147603744953057279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.039 Γ— 10⁹⁷(98-digit number)
10397852035767373893…11147603744953057281
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
2.079 Γ— 10⁹⁷(98-digit number)
20795704071534747787…22295207489906114559
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:57,786,631 XPMΒ·at block #6,817,820 Β· updates every 60s
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