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Block #2,633,921

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 4:19:44 PM Β· Difficulty 11.2155 Β· 4,208,382 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ed7acdee120d35ef23554551d024897e631c2bfcc08ce3cb7370e6f609a673d7
View on Chainz β†—

Height

#2,633,921

Difficulty

11.215470

Transactions

2

Size

573 B

Version

2

Bits

0b372908

Nonce

417,237,657

Timestamp

4/28/2018, 4:19:44 PM

Confirmations

4,208,382

Mined by

⛏️ P2SHAL8kQ7fqdHdrZsHttWBtbLVQZKW7k51kkG

Merkle Root

c78fccc5bf9e4994feb633f15f97c13b51bc5c9e0aa65462325cd09e1da7d702
Transactions (2)
Coinbasea3ee667e67f86b…a19718ebe43981
1 in β†’ 1 out7.9500 XPM110 B
AL8kQ7fq…W7k51kkG
9bcfa06618c0ca…9cc534fe9e5b45
2 in β†’ 2 out5.0130 XPM373 B
AGmUwXS2…bscQCJ7GAUHK7JFZ…x3Pkbnyf
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.

3.459 Γ— 10⁹⁴(95-digit number)
34591189140544112215…67925533610497238399
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
3.459 Γ— 10⁹⁴(95-digit number)
34591189140544112215…67925533610497238399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.459 Γ— 10⁹⁴(95-digit number)
34591189140544112215…67925533610497238401
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
6.918 Γ— 10⁹⁴(95-digit number)
69182378281088224431…35851067220994476799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.918 Γ— 10⁹⁴(95-digit number)
69182378281088224431…35851067220994476801
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
1.383 Γ— 10⁹⁡(96-digit number)
13836475656217644886…71702134441988953599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.383 Γ— 10⁹⁡(96-digit number)
13836475656217644886…71702134441988953601
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
2.767 Γ— 10⁹⁡(96-digit number)
27672951312435289772…43404268883977907199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.767 Γ— 10⁹⁡(96-digit number)
27672951312435289772…43404268883977907201
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
5.534 Γ— 10⁹⁡(96-digit number)
55345902624870579544…86808537767955814399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.534 Γ— 10⁹⁡(96-digit number)
55345902624870579544…86808537767955814401
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
1.106 Γ— 10⁹⁢(97-digit number)
11069180524974115908…73617075535911628799
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:57,982,829 XPMΒ·at block #6,842,302 Β· updates every 60s
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